تعريف الدالة. دالة رياضية

Dubinsky, Ed; Harel, Guershon 1992 , The Concept of Function: Aspects of Epistemology and Pedagogy, Mathematical Association of America, ISBN 0883850818 Katz, Robert 1964 , Axiomatic Analysis,
If the function f x is even, a cosine input will produce no odd harmonics but may contain a DC component

Wherein Russell announces his discovery of a "paradox" in Frege's work.

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تحديد مجموعة تعريف دالة ( عموميات حول الدوال )
If the function is neither odd nor even, all harmonics may be present in the output
شارح الدرس: تعريف المشتقة
Gottlob Frege 1879 Begriffsschrift, a formula language, modeled upon that of arithmetic, for pure thought with commentary by van Heijenoort, pages 1—82• Ernst Zermelo 1908a Investigations in the foundations of set theory I, with commentary by van Heijenoort, pages 199—215
دالة الـSUM في الإكسيل: تعريفها وكيفية استخدامها وأمثلة عملية
, New York NY, ISBN 0-486-24004-5
, a Java applet for exploring functions graphically Suppes, Patrick 1960 Axiomatic Set Theory, Dover Publications, Inc, New York NY, ISBN 0-486-61630-4
Mineola, NY, ISBN 0-486-69609-X pbk• gives formulae and visualizations of many mathematical functions Bertrand Russell 1902 Letter to Frege with commentary by van Heijenoort, pages 124—125

David Hilbert 1904 On the foundations of logic and arithmetic, with commentary by van Heijenoort, pages 129—138.

تعريف الدوال وانواعها
1980 , "Historical and pedagogical aspects of the definition of function", International Journal of Mathematical Education in Science and Technology 11 4 : 489—492, :
دالة أم ليست دالة worksheet
Wherein von Neumann creates "classes" as distinct from "sets" the "classes" are Zermelo's "definite properties" , and now there is a universal set, etc
تحديد مجموعة تعريف دالة ( عموميات حول الدوال )
1879 , Begriffsschrift: eine der arithmetischen nachgebildete Formelsprache des reinen Denkens, Halle• Giuseppe Peano 1889 The principles of arithmetic, presented by a new method with commentary by van Heijenoort, pages 83—97• , New York, NY ISBN 0-486-28462-x• 1, Cambridge at the University Press, Cambridge, UK, republished as a googlebook